Lecture 3 - Carnot Cycle

Question 1

How is the SFEE written for boilers and condensers, and why?

Answer 1

DetlaQ = h2-h1

They do no work on the fluid

Question 2

How is the simplified SFEE written for turbines and compressors, and why?

Answer 2

-DeltaW = (h2-h1)
Kinetic energy changes are negligible so neglected
Processes are adiabatic (no heat transfer)

Question 3

What equation can be used on a perfect gas in a turbine or compressor?
(Give rearranged version too)

Answer 3

cp = (dh/dT)p
Can also be written as
h2-h1 = cp(T2-T1)

Question 4

How is the SFEE written for nozzles and diffusers?

Answer 4

(0.5C2^2-0.5C1^2) = (h1-h2)

Question 5

Why can’t kinetic energy be neglected in the SFEE for nozzles and diffusers?

Answer 5

In these devices they may become significant terms

Question 6

Why does the Carnot cycle accept heat at one max temp and reject it at a fixed lower temp?

Answer 6

The larger the average temperature difference, the greater the efficiency of the cycle. This system maintains the highest difference.

Question 7

Which components are involved in the Carnot cycle?

Answer 7

Pump, boiler, turbine, condenser

Question 8

What is required for an ideal thermodynamic cycle in the Carnot cycle?

Answer 8

Reversible isothermal processes

Reversible adiabatic processes (compression and expansion) - ie isentropic process

Question 9

How would an ideal thermodynamic cycle be achieved in the Carnot cycle?

Answer 9

Using a fluid which is a condensable vapour.

Isothermal processes carried out at constant pressure and temperature, working fluid changes state

Question 10

On a T-s diagram,, what are

4-1, 1-2, 2-3, 3-4?

Answer 10

4-1: pump, isentropic
1-2: boiler, isothermal
2-3: turbine, isentropic
3-4: condenser, isothermal

Question 11

Give the SFEE for all processes of the Carnot cycle

Answer 11

Boiler: Q1-2 = h2-h1
Turbine: W2-3 = h3-h2
Condenser: Q3-4 = h4-h3
Pump: W4-1 = h4-h1

Question 12

What is represented by:

T, s, h, Q, W, cp, U?

Answer 12

T = Temperature
s = entropy 
h = enthalpy 
Q = heat transferred 
W = work transferred 
U = internal energy

Question 13

How is an ideal component’s thermodynamic state designated?

Answer 13

By a prime (ie 1’ for position 1) next to the actual numerical value on the graph

Question 14

How does entropy change in ideal vs non-ideal fluid processes?

Answer 14

Ideal: no change

Non-ideal: increases

Question 15

The higher the value of X, the more efficient the cycle.

What is X?

Answer 15

The maximum temperature

Question 16

What is the temperature at which heat is rejected from the cycle at governed by?

Answer 16

Atmospheric considerations, ie temp difference between working fluid and sink

Question 17

What is the maximum working temperature of the Carnot cycle governed by?

Answer 17

Strength of materials- must be able to withstand pressures

Question 18

Why can the Carnot cycle not make the best use of material limits?

Answer 18

To operate in the wet region, the temp is limited to critical temp, 374C, whereas the materials can withstand 550-600C.

Question 19

What are the problems with using a mixture of liquid and vapour?

Answer 19

Impossible to get pump that works on two phase fluid

Liquid droplets can damage turbine blades due to high speeds

Question 20

Draw a Ts diagram of a carnot cycle?

Answer 20

Square box

1) isothermal expansion
2) Adiabatic expansion
3) Isothermal Compression
4) Adiabatic Compression

Question 21

Draw a pressure volume diagram of a carnot cycle?

Answer 21

1) isothermal expansion
2) Adiabatic expansion
3) Isothermal Compression
4) Adiabatic Compression

Question 22

How can you determine the properties of the fluids at different points within the carnot cycle?

Answer 22

If on saturated line - either completely liquid or vapour

Isentropic process therefore entropy will be the same at inlet and outlet of turbine and at the inlet and outlet of pump

Question 23

How can the wetness/dryness fraction initially be determined?

Answer 23

by using the known entropy of the fluid and calculating with the saturated entropy of the liquid and steam at that pressure

Question 24

What is the net work output of the carnot cycle?

Answer 24

Energy out of turbine - energy into pump

h2 - h3) - (h1 - h4

Question 25

What is the efficiency of the carnot cycle?

Answer 25

Net work out/Heat in or simplified to

Thot - Tcold / Thot

Question 26

How are turbine and compressor efficiencies taken into account

Answer 26

for turbine - change in enthalpy * efficiency - get less work out
for compressor - change in enthalpy/efficiency - have to put more work in